Chapter 2 Forces and Motion

2.12 Elasticity

2.12 Elasticity

2.12 ElasticitySome common devices like eraser

and ruler will change its shape when external force acting on it.

A rubber band is elastic. You can stretch it and once you let go it will return to its original shape.

2.12 ElasticityThe property of an object that enables

it to return to its original shape and dimensions after an applied external force is removed is called elasticity.

Jello is elastic.

2.12 Elasticity

HOOKE’S LAW

2.12 Elasticity

HOOKE’S LAWstates that the extension of a spring is directly proportional to the applied force provided that the elastic limit is not exceed.

2.12 Elasticity

HOOKE’S LAWElastic limit the maximum force that can be applied to a spring such that the spring will be able to be restored to its original length when the force is removed.

2.12 Elasticity

HOOKE’S LAW

2.12 Elasticity

HOOKE’S LAWstates that the extension of a spring is directly proportional to the applied force provided that the elastic limit is not exceed.

kxFxF

* k is constant of the spring, with unit N/m

2.12 Elasticity

HOOKE’S LAWSpring constant, k, is a measurement of

the stiffness of the spring.

A spring with a spring constant 12 N/m requires a force of 12 N to produce an extension 1 m.

2.12 Elasticity

HOOKE’S LAW

2.12 Elasticity

HOOKE’S LAWExampleThe length of a spring is increased from 23.0 cm to 28.0 cm when a mass of 4 kg was hung from the end of a spring.(a) What the load on the spring in newtons? (b) What is the extension of the spring? (c) Calculate the force constant of the spring (Assume g = 10 N/kg)

2.12 Elasticity

HOOKE’S LAWSolution(a) 4(10) = 40 N(b) 28.0 cm – 23.0 cm = 5.0 cm(c) F = kx

k = F/xk = 40 / 5k = 8 N/cm

2.12 Elasticity

HOOKE’S LAW

Experiment on Hooke’s law (.doc)

2.12 Elasticity

SYSTEM OF SPRINGS

2.12 Elasticity

Two springs can be connected in series or in parallel.

2.12 Elasticity

When two springs are connected in series, the applied force acts on each spring. Each spring experience a force/tension of 30 N.

2.12 Elasticity

When two springs are connected in parallel, the applied force is shared equally among the springs. Therefore each spring experience a force/tension of 60 N.

2.12 ElasticityExampleThe figure shows a spring extends by 1 cm when an 8 N force is applied on it. Similar springs used to set up three systems. Calculate the total extensions in each system.

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SolutionTotal extension in system PQ = 2 cmRS = 0.5 cmTUV = 1.5 cm

2.12 ElasticityExampleThe figure shows three identical springs.What is the value of Y?

2.12 Elasticity

SolutionForce on the spring, F = 10 N, x = 2 cm

1-cm N 52

10

xFk

kxF

2.12 Elasticity

SolutionTwo springs share the load of 40 N, therefore the force on each spring is 20 N.

cm 4520

kFy

kyF

2.12 Elasticity

ELASTIC POTENTIAL ENERGY

2.12 ElasticityELASTIC POTENTIAL ENERGY

The energy stored in a spring when it is extended or compressed.

2.12 ElasticityELASTIC POTENTIAL ENERGY

When a force extends a spring, work is done.

The work done on the spring is the energy transferred to the spring and stored as elastic potential energy.

2.12 ElasticityELASTIC POTENTIAL ENERGY

The elastic potential energy stored in a stretched spring is given by

2

21 kxEP

* Unit is Joules (J)

2.12 ElasticityELASTIC POTENTIAL ENERGY

2.12 ElasticityELASTIC POTENTIAL ENERGY

ExampleA 2 kg load is hung from the end of a spring with a spring constant of 160 N/m.(a) What is the tension of the spring?(b) What is the extension of the

spring?(c) Calculate the elastic potential

energy stored in the spring.[Assume g = 10 N/kg]

2.12 ElasticityELASTIC POTENTIAL ENERGY

Factors that influence the elasticity of a springType of spring material

A spring made from hard material requires a larger force to stretch it. Hence the spring constant, k is greater.

2.12 ElasticityELASTIC POTENTIAL ENERGY

Factors that influence the elasticity of a springDiameter of the coil of spring

A spring made of a larger diameter coil is softer.

2.12 ElasticityELASTIC POTENTIAL ENERGY

Factors that influence the elasticity of a springDiameter of the wire of the spring

A spring coil of spring made from thicker wire is more difficult to stretch than a coil spring made from wire that is thinner.

2.12 ElasticityELASTIC POTENTIAL ENERGY

Factors that influence the elasticity of a springArrangement of the spring

A longer spring is easier to stretch compared to a shorter spring.

Springs arranged in series are easier to stretch when compared to springs arranged in parallel.